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IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com

IJERA (International journal of Engineering Research and Applications) is International online, ... peer reviewed journal. For more detail or submit your article, please visit www.ijera.com

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  • 1. Ezhilarasi .P, Dr.Nirmal Kumar .P / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1675-1681 An Efficient Image Compression By Overlapped Discrete Cosine Transform With Adaptive Thinning Ezhilarasi . P *, Dr.Nirmal Kumar .P ** *( Department of ECE, St.Joseph’s College of Engineering , Anna University, Chennai,India,) ** (Department of ECE College of Engineering Guindy, Anna University, Chennai, India,)ABSTRACT With the development of network and reduction in file size allows more images to bemultimedia technology, real time image stored in a given amount of disk or memory space. Itacquisition and processing is becoming a also reduces the time required for images to be sentchallenging task because of higher resolution, over the internet or downloaded from Web pages.which imposes very high bandwidth requirement. There are so many different ways available toImage compression is the only way to meet this compress the image files. For the usage of internet,requirement. The objective of image the two most common compressed graphic imagecompression is to reduce redundancy of the formats are the GIF format and the JPEG format.image data in order to able to store or transmit The GIF method is commonly used for line art anddata in an efficient form. This paper proposes a other images in which geometric shapes areconcept for digital image compression. The relatively simple whereas the JPEG method is moreresulting compression scheme relies on often used for photographs. Other two techniques ofoverlapped (modified) discrete cosine transform image compression are the use of fractals andwhich is based on the type IV Discrete cosine wavelets. These methods have not gainedtransform(DCT-IV) with the additional property widespread acceptance for use on the internet.of being lapped is proposed enabling a robust and However, both methods promise that they offercompact image compression and adaptive higher compression ratios than the JPEG or GIFthinning algorithms are recursive point removal methods for some types of images.schemes, which are combined with piecewiselinear interpolation over detrimental Delaunay Image-compression algorithms are broadlytriangulations. Simulation result shows that classified into two categories depending whether orcompression of image done in this way enables not an exact replica of the original image could bemore than 80% pixel level memory reduction at a reconstructed using the compressed image. They arepeak signal-to-noise ratio level around 30 dB and lossy and lossless. In lossy image-compression, thereless recursive points to produce a compressed is a trade off between the compression ratio and theimage reconstructed image quality. If the distortion due to compression is tolerable, the increase inKeywords— Image compression, modified compression ratio becomes very significant. Lossydiscrete cosine transform (MDCT), Thinning, image-compression algorithms can be performed inDelaunay triangulation either spatial domain or transform domains (frequency domain). Here limited bits are used toI. INTRODUCTION quantise the predictive value. There are different Image compression is a vital area which effective predictors, such as the gradient-adjustedaddresses the problem of reducing the amount of predictor (GAP) [8] and the median adaptivedata required to represent a digital image. It is a predictor (MAP) [9]. Another way to compress theprocess intended to yield a compact representation image is to firstly map the image into a set ofof an image, thereby reducing the image storage and transform coefficients using a linear, reversibletransmission requirements. Various image transform, such as Fourier transform, discrete cosinecompression methods were proposed and developed transform or wavelet transform. The newly obtainedas standards such as the joint photographic experts set of transform coefficients are then quantized andgroup (JPEG) standards [1] &[2], the discrete cosine encoded.transform (DCT)-based coding [3],[4]&[5], thewavelet-based coding [6]&[7] because of extensive In transform coding scheme, transformsresearch carried out in the field of image such as DFT (Discrete Fourier Transform) and DCTcompression. (Discrete Cosine Transform) are used to change the pixels in the original image into frequency domain Image compression is minimizing the size coefficients (called transform coefficients). Thesein bytes of a graphics file without degrading the coefficients have several desirable properties. One isquality of the image to an unacceptable level. The the energy compaction property that results in most 1675 | P a g e
  • 2. Ezhilarasi .P, Dr.Nirmal Kumar .P / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1675-1681of the energy of the original data being concentrated II. RELATED WORKin only a few of the significant transform Different compression schemes arecoefficients. This is the basis of achieving the proposed by different groups of researchers overcompression. Only those few significant coefficients modified discrete cosine transform based imageare selected and the remaining is discarded. The compression and adaptive thinning. Both theselected coefficients are considered for further compression techniques are used separately and lotquantization and entropy encoding. DCT coding has of improvement are achieved by differentbeen the most common approach in transform researchers group in terms of low or no losscoding. It is also adopted in the JPEG image compression, speedy compressioncompression standard. Che-Hong Chen , IEEE et.al [11] have presented efficient recursive architectures for realizing the Lossless image-compression algorithms are modified discrete cosine transform (MDCT) and theerror-free compression, which are widely used in inverse MDCT (IMDCT) acquired in many audiomedical applications, satellite imagery, business coding systemsdocumentation, and radiography area because any Rene J. van der Vleuten, IEEE et.al [13]information loss is undesirable or prohibited. have developed a scalable image compressionThe performance of any image compression scheme scheme with a good performance-complexity trade-depends on its ability to capture characteristic off. Like JPEG, it is based on the 8 x 8 blockfeatures of the image, such as sharp edges and fine discrete cosine transform (DCT), but it uses notextures, while reducing the number of parameters additional quantization or entropy coding bit rate .used for its modelling. The `compression standard Ezhilarasi.P et.al IETE [12] have discussed aboutJPEG2000 uses contextual encoding, which models adaptive thinning algorithm which uses Delaunaythe Markovian structures in the pyramidal wavelet triangulations method to remove the recursive pointdecomposition of the image at very low bit rates, in the image.however, the oscillatory behaviour of wavelet bases Shizhong Liu, Student Member, IEEE et.altypically leads to undesirable artefacts along sharp [14] have modelled blocking artifacts as 2-D stepedges[10]. functions. In which a fast DCT-domain algorithm is proposed which extracts all parameters needed to In many classical image compression detect the presence of, and estimate the amplitude ofmethods, such as for the aforementioned DCT and blocking artifacts, by exploiting several properties ofDWT, the modelling is carried out by decomposing the human vision system.the image over a non-adaptive orthogonal basis of Jian Huang et.al [15] have proposed FPGA-functions. The corresponding coefficients of the based scalable architecture for DCT computationbasis functions are then quantised, according to a using dynamic partial reconfiguration. Which canspecific quantisation step, which usually depends on perform DCT computations for eight different zones,a target compression rate. The performance of the i.e., from 1x1 DCT to 8x8 DCTresulting compression scheme depends on theapproximation quality which results from the non- The proposed work involves the following steps:vanishing coefficients. 1) The MDCT is two dimensional discrete cosine transform implementation which is based on The proposed compression algorithm which the type IV Discrete cosine transform(DCT-IV) withcombines MDCT[11] and adaptive thinning the additional property of being lapped is proposedalgorithms[12]. In first phase of encoding, the enabling a robust and compact image compressionmodified discrete cosine transform which is based [11].on the type IV Discrete cosine transform(DCT-IV) 2) Adaptive thinning algorithm is employedwith the additional property of being lapped is which uses Delaunay triangulations method toproposed enabling a robust and compact image remove the recursive point in the image and also tocompression .In second phase of encoding, process the image further easily since the thinnedcompression scheme relies on adaptive thinning image dealing only with edges[12].algorithms, which are used to remove the recursive 3) Integration of all above methods is done topoints. achieve less memory requirement, less recursive points, higher compression ratio and PSNR. The rest of the paper is organised into 7 sections.Section II describes the related works. Section III III.MDCTpresents the modified discrete cosine transform Joint Photographic Experts Group (JPEG)compression algorithm. Section IV explains the is a commonly used standard technique ofthinning methodology and associated compression compression for photographic images which utilizesalgorithm. Section V gives the integration of MDCT DCT. DCT separates images into parts of differentand thinning. Section VI discusses the simulation frequencies (i.e. dc & ac components) where lessresults .Section VII concludes this paper. important frequencies are discarded through 1676 | P a g e
  • 3. Ezhilarasi .P, Dr.Nirmal Kumar .P / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1675-1681quantisation and important frequencies are used to In the case of JPEG an 8 x 8 block of pixels isretrieve the image during decompression. Currently mapped to an 8 x 8 block of frequencythe standard Discrete Cosine Transformation components ,meaning that the amount of data to be(DCT) based algorithm of the JPEG is the most entropy coded(output of DCT) is same as thewidely used and accepted for image compression. original amount of data (input to the DCT). ThisIt has excellent compaction for highly correlated desirable property is referred to as critical sampling.data. DCT separates images into parts of In the case of overlap-and- add (with 50% overlap),different frequencies where less important the transform block will have twice as many asfrequencies are discarded through quantisation and blocks (of the same size) it has before or withoutimportant frequencies are used to retrieve the overlapping. In this process the amount of data to beimage during decompression [16]. Compared to compressed has thus doubled, and critical samplingother input dependent transforms, DCT has many is lost. The modified discrete cosineadvantages: (1) It has been implemented in single transform(MDCT) overcomes this problem: whereasintegrated circuit, (2) It has the ability to pack a standard DCT would map N samples of data to Nmost information in fewest coefficients But the new values, the MDCT maps an N-sample block,disadvantage of DCT scheme is the “blockingartifacts” in reconstructed image at high say x, to a block consisting of new values, say X,compression ratio which degrades quality of as illustrated in the below figure.reconstructed image. Also in DCT, edges of thereconstructed image are blurred but smooth. The Forward MDCT Inverse MDCTabove drawbacks are eliminated by MDCT which is N/2 N Nbased on a DCT of overlapping data. The modified discrete cosine transform Figure.1. A block diagram description of the(MDCT) is a Fourier-related transform based on the forward and inversetype-IV discrete cosine transform (DCT-IV), with MDCTthe additional property of being lapped: it is The 8 x 8 blocks of frequency componentsdesigned to be performed on consecutive blocks of a are quantised by using the existing 1D case of 16-larger dataset , where subsequent blocks are sample transform blocks illustrated with twooverlapped so that the last half of one block dimensions to retain the JPEG’s existing well-coincides with the first half of the next block. This defined structure. The 16 x 16 blocks of pixels willoverlapping, in addition to the energy-compaction be applied first to its row, and then to the column ofqualities of the DCT, makes the MDCT especially the resulting 16 x 16 matrix, there by implementingattractive for image compression applications, since a 2D windowed MDCT. This transform thereforeit helps to avoid artifacts stemming from the block maps 16 x 16 transform blocks to 8 x 8 blocks ofboundaries. frequency components. Similarly using the 2D inverse transform it will be mapped back to 16 x 16 As a lapped transform, the MDCT is a bit blocks. This concept is illustrated in the below blockunusual compared to other Fourier-related diagram.transforms in that it has half as many outputs as MDCT IMDCTinputs (instead of the same number). In particular, itis a linear function F: R2N → RN (where R denotes 16 x 16 8x8 16 x 16the set of real numbers). The 2N real numbers x0, ...,x2N-1 are transformed into the N real numbers X0, ...,XN-1 according to the formula: Figure2: Extending the IMDCT to two dimensions in order to obtain 8 x 8 transform blocks -- (1) By doing this, overlap adding is also The inverse MDCT is known as the extended to two dimensions. Each 2D transformIMDCT. The perfect invertibility is achieved by block will have 8 neighbouring blocks to overlapadding the overlapped IMDCTs of subsequent with. Alternatively one could first apply to each rowoverlapping blocks, causing the errors to cancel and of an entire image; the same is then done to columnsthe original data to be retrieved. of the resulting output. In the end the same matrixThe IMDCT transforms N real numbers X0, ..., XN-1 say Y, consisting of 8 x 8 blocks of frequencyinto 2N real numbers y0, ..., y2N-1 according to the components is obtained. To decode, the reverseformula: process is applied, the first each column of Y is inversely transformed by overlapped and added then to the each row of the resulting output. By retaining -(2) 8 x 8 blocks of frequency components, the overall operation of DCT is retained by MDCT. The MDCT 1677 | P a g e
  • 4. Ezhilarasi .P, Dr.Nirmal Kumar .P / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1675-1681coefficients in an 8 x 8 block are roughly 4 timeslarger than DCT coefficients in an 8 x 8 blocks.Algorithm 1: Original image is divided into blocks of 8 x 8. 2: Pixel values of a grey image ranges from 0-255but MDCT is designed to work on pixel valuesranging from -128 to 127. Therefore each block ismodified to work in the range.3: The transform blocks are formed using 50% Figure 3: Removal of the vertex y, andoverlap retriangulation of its cell. The five triangles of the4: Then normalized window function is applied to cell in (a) are replaced by the three triangles in (b).the blocks. A linear spline is a continuous function, which is5: Time to frequency mapping is applied to these piecewise linear over a partitioning of its domain Ωblocks, resulting in frequency components. € R2. Let the domain coincide with the convex hull6: The frequency components are quantized & [X] of the input point set X. If the convex hull [Y] ofentropy encoded any subset Y  X, constructed by thinning,7: The reverse process is done to obtain the coincides with the convex hull of X and ensured thatdecompressed image external points not removed from X. A convenient choice for the partitioning of Ω is the DelaunayIV.ADAPTIVE THINNING triangulation D(Y) of Y . Adaptive thinning constructs a hierarchy ofsets of the most significant pixels, where for each set Firstly, a Delaunay triangulation D(Y) of athe image is approximated by the linear spline over finite planar point set Y is one, such that for anythe Delaunay triangulation of the pixels in the set. triangle in D(Y) its corresponding circumferenceGeneric Formulation of Thinning: does not contain any point from Y in its interior.Let X ={X1,….,XN}  R2 denote a finite This property is termed as the Delaunay property. 2 Moreover, there is a unique triangulation of Y withscattered point set in R , and let fX = (f(x1), . . . ,f(xN))T € RN denote a corresponding data vector the Delaunay property, provided that no four pointscontaining point samples taken from an unknown in Y are co-circular. It is assumed that this conditionfunction f : R2  R at the points of X. Thinning is a on the given set X in order to avoid lengthy butrecursive point removal scheme for bivariate immaterial discussions concerning the non-scattered data, whose generic formulation is given uniqueness of D(Y), for Y  X.by the following algorithm, where n is the number of `Secondly, it is noted that the removal of one point yremovals[10]. from Y requires an update of D(Y) in order to obtainAlgorithm the Delaunay triangulation D(Y y). Due to the(1) Let XN = X Delaunay property, this update of D(Y) is local.(2) FOR k = 1, . . . , n Indeed, the required retriangulation, incurred by the(3) Locate a removable point x Xk removal of the vertex y in D(Y), can be performed(4) Let XN−k = XN−k+1 x; by the retriangulation of its cell C(y). It is recalled XN−n ·· · XN−1 XN = X ---(3) that the cell C(y) of y is the union of all triangles in Note that thinning constructs, for given data D(Y) which contain y as a vertex. Figure 3(a) & 3(b)(X, fx), a nested sequence of subsets of X, where the shows, for a vertex y in a Delaunay triangulation, thesize |Xk| of any subset Xk in (1) is k, N−n ≤ k ≤ N. retriangulation of its cell C(y)Two consecutive subsets in equation (3) differ onlyby one point. In order to select a specific thinning V.INTEGRATION OF MDCT &strategy, it remains to give a definition for a THINNINGremovable point in step (3) above. Basic operation of the whole framework can be seen as the combined effect of MDCT and To remove the recursive points in the image Adaptive Thinning methods. The functional blockwe use the Delaunay triangulations method as shown diagram is given in figure 4.in the figure below if we remove the vertex y fromfigure 3(a) the actual structure of the pentagonmentioned as before externally as shown in figure3(b) and ensured that external points not removedfrom figure. 1678 | P a g e
  • 5. Ezhilarasi .P, Dr.Nirmal Kumar .P / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1675-1681 image of size 7KB in JPEG format as shown in figure7. Since we use thinning operation, the grey scale image is required to be converted into monochrome image which is shown in figure 8 and then it is fed to Thinning block. Finally the thinned image output is given in figure 9 whose size is 57KB and it has less recursive points. By employing both the methods mentioned in this paper, both less memory space and less recursive points can be achieved.Figure 4: Functional block diagram In the first phase of encoding, the modifieddiscrete cosine transform which is based on the typeIV Discrete cosine transform(DCT-IV) with theadditional property of being lapped is proposedenabling a robust and compact image compression.Here the original lena image of 147 kB is Figure 5: Original lena imagecompressed in to 7 kb image with compression ratioof 40 at PSNR around 30 dB. In the second phase of encoding,compression scheme relies on adaptive thinningalgorithms, which are recent multiresolutionmethods from scattered data approximation.Adaptive thinning algorithms are recursive pointremoval schemes, which are combined with Figure 6: MDCT blocked imagepiecewise linear interpolation over decrementalDelaunay triangulations [9]. Here the compressedlena grey scale image is appeared as the thinnedimage of 57 kB which has less recursive points. By combining the modified discrete cosinetransform and thinning compression scheme, thememory size could be reduced which is taken careby the MDCT and the output of MDCT encoderimage is again decoded back and this image is fed asinput to thinning image model which further Figure 7: Compressed lena imageconverters grey scale image into monochrome imagethat removes the recursive points from the encodedcompressed image that makes regeneration of imageby using minimal numbers of parameters of imageduring decoding . Here the output is monochromeimage and it can be transmitted fast on networkbecause here complexity is less as compared to othercoding schemes. In is method we have two differentoutput one is greyscale image format that from Figure 8: Monochrome image of figure 7.MDCT and another from Thinning module outputthat is monochrome but both images are incommercial standard JPEG2000 [10].VI. SIMULATION RESULTS As the original image shown in figure 5 isof 147KB is the CCD output which is in the PNGformat and it is fed as the input to MDCT blockencoder and its output is shown in figure 6 which isin the blocked format of homogenous type and Figure 9: Thinned Image of the compressed imagehaving a limit of block size 8x8. Then it is fed intothe MDCT decoder which generates the compressed 1679 | P a g e
  • 6. Ezhilarasi .P, Dr.Nirmal Kumar .P / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1675-1681Thus 147 KB original image is compressed to 7 KBat PSNR ratio around 30 dB in MDCT compressionschemeand 57 KB in Thinning method .The peak signal-to-noise ratio of cameraman image obtained for variouscompression methods are listed below in table1. Method PSNR DCT 19.28 Wavelet 26.78 MDCT 29.1965Table 1. Comparison of PSNR for variouscompression algorithm Figure 11: CR Vs PSNR for lena imageThe comparison of PSNR chart for various The comparison study of DCT,DWT & MDCT arecompression methods (DCT, DWT & MDCT) are depicted in figure 12 which shows better PSNRshown in figure 10. values for proposed method MDCT. Figure 12: PSNR values for DCT,DWT&MDCT Figure 10: Comparison of PSNR forcameraman image. The compression ratio and psnr values for threeThe relationship between compression ratio and different images along compression size in MDCTPSNR for lena image for proposed algorithm is and thinning algorithm is given in table 2.plotted in figure 11. Original MDCT Thinning Compression PSNR Original Image S.No. Image Size Size JPEG Size JPEG ratio In dB 1. TIFF 77 3 19 24.5631 29.1965 KB KB KB 2. PNG 147 7 57 39.7489 29.5663 KB KB KB 3. GIF 292 7 90 39.7489 29.5635 KB KB KB Table 2. Image compression for differentimagesVII.CONCLUSIONS This method generates three different images of a This paper reports the integration of two single raw image .They are: (1) Lena gray scalecompression schemes based on modified discrete image in PNG format that is compressed by MDCT,cosine transform compression and adaptive thinning. (2) the image in the monochrome format, (3) thinned 1680 | P a g e
  • 7. Ezhilarasi .P, Dr.Nirmal Kumar .P / International Journal of Engineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.com Vol. 2, Issue 5, September- October 2012, pp.1675-1681image. Since all the images are in JPEG2000 format [9] D. D. Estrakh, H. B. Mitchell, P. A.and require very less memory as compared to other Schaefer, Y. Mann, Y. Peretz. "Soft mediancompression technology and also here it is proved adaptive predictor for lossless picturethat the high PSNR is obtained compared to DCT & compression.”, Journal of signalDWT. The compression can be controlled by Processing, 2001: 1985~1989changing compression ratio in MDCT. Since thinned [10] Laurent Demaret and Armin Iskeimage is dealing with only edges of the objects in the Zentrum ,”Advances in Digital Imageimage, further processing is very easy and fast Compression by Adaptivebecause it contains minimum information about Thinning”,Mathematik, Technischeimage and also it removes the recursive points. This Universit at Munchen, D-85747 Garching,new method is very useful for image or video based Germany- 2009.tracking and edge based tracking for the real time [11] Che-Hong Chen, Bin-Da Liu, Seniorapplication where processor capabilities are limited Member, IEEE, and Jar-Ferr Yang, Seniorand minimum. The simulation results illustrate that Member, “Recursive Architectures forthe proposed algorithm results in more than 80% Realizing Modified Discrete Cosinepixel level memory reduction at a peak signal-to- Transform and Its Inverse” , IEEE, trans onnoise ratio level around 30 dB and less recursive circuits and systems-II,January 2003points to generate a compressed image.In future [12] P.Ezhilarasi, and P.Niemal Kumar ,thinned image size is further reduced by using any of “ Integrated Image compression bythe morphological operations. Predictive Boundary Adaptation with QTD and adaptive Thinning”, IETE internationalREFERENCES conference ACCT-2012,Feburary. [1] W. Pennebaker and J. Mitchell, JPEG Still [13] Rene, J . Vander vleuten Richard I Image Data Compression Kleihorstt Christian Hentschelt, “low- Standard.(Springer ,31-December -1992- complexity scalable dct image 650 pages). compression”, IEEE international [2] Gregory K. Wallace, “The JPEG Still conference , 2000 Picture Compression Standard ,Multimedia [14] Shizhong Liu, Student Member, IEEE, and Engineering”, Digital Equipment Alan C. Bovik, Fellow, “Efficient DCT- Corporation Maynard, IEEE Transactions Domain Blind Measurement and Reduction on Consumer Electronics. December 1991 of Blocking Artifacts “,Laboratory for “PDCA12-70 data sheet,” Opto Speed SA, Image and Video Engineering Dept. of Mezzovico, Switzerland Electrical and Computer Engineering The [3] N. Ahmed, T. Natarajan, and K. R. Rao, University of Texas at Austin, Austin, TX “Discrete cosine transform,”IEEE Trans. 78712-1084, USA Comput., vol. C-23, no. 1, pp. 90–93, Jan. [15] Jian Huang, Matthew Parris, Jooheung Lee, 1974. and Ronald F. DeMara University of [4] K. Rose, A. Heiman, and I. Dinstein, Central Florida “Scalable FPGA-based “DCT/DST alternate-transform image Architecture for DCT Computation Using coding,” IEEE Trans. Commun., vol. 38, no. Dynamic Partial”, ACM Trans. Vol. 5 , 1, pp. 94–101, Jan.1990. December 2008. [5] Andrew B. Watson NASA Ames Research [16] Ze-N ian li,Marck.S.Drew, Fundamentals center, “Image Compression Using Discrete of Multimedia (PHI Education). Cosine Transform”, Mathematical Journal, 4 (1) ,1994 , P. 81-88 [6] A. E. Cetin, O. N. Gerek, and S. Ulukus, “Block wavelet transforms for image coding,” IEEE Trans. Circuits Syst. Video Technol., vol. 3, no. 6, pp. 433–435, Dec. 1993. [7] Sonja Grgic, Mislav Gric,”Performance analysis of image compression using wavelets”, transactions on Industrial Electronics,Vol.48,no.3,June 2001 [8] Ng,K.S. Cheng,L.M. “Lossless image compression by using gradient adjusted prediction and Burrows-Wheeler transformation”, IEEE Transactions on Consumer Electronics, Volume: 45: issue 2 On page(s): 380 – 386, May 1999 1681 | P a g e